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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Brauer-Manin obstruction on algebraic stacks
代数栈 Brauer-Manin阻塞 Hasse原理
2023/11/29
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
Essential dimension is a numerical invariant of an algebraic
group G introduced by J. Buhler and the second author to study the
complexity of G-torsors over a eld K. It has since been studied by se...
ESSENTIAL DIMENSION OF MODULI OF CURVES AND OTHER ALGEBRAIC STACKS (WITH AN APPENDIX BY NAJMUDDIN FAKHRUDDIN)
ESSENTIAL DIMENSION OTHER ALGEBRAIC STACKS
2015/9/29
In this paper we consider questions of the following type.
Let k be a base eld and K=k be a eld extension. Given a geometric
object X over a eld K (e.g. a smooth curve of genus g) what is the
le...
For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent s...
Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system
Toric Deligne-Mumford stacks GKZ hypergeometric system Algebraic Geometry
2012/5/9
We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in the...
Toric Stacks II: Intrinsic Characterization of Toric Stacks
Toric Stacks II fan stack moduli Algebraic Geometry
2011/9/1
Abstract: The purpose of this paper and its prequel (Toric Stacks I) is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks defined in [Laf02, B...
Toric Stacks I: The Theory of Stacky Fans
Toric Stacks I The Theory of Stacky Fans Algebraic Geometry
2011/9/1
Abstract: The purpose of this paper and its sequel (Toric Stacks II) is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks defined in [Laf02, B...
Quivers of sections on toric Deligne-Mumford stacks
Quivers of sections toric Deligne-Mumford stacks
2011/1/21
Starting from a collection of line bundles on a smooth projective toric DM stack,we give a stacky analogue of the classical linear series construction. We apply our construction to recover the finite ...
This is the first in a projected series of three papers in which we construct the second flip in the log minimal model program for Mg. We introduce the notion of a weakly proper algebraic stack.
Partial desingularizations of good moduli spaces of Artin toric stacks
Partial desingularizations good moduli spaces of Artin toric stacks
2011/1/19
Let X be an Artin stack with good moduli space X → M. We define the Reichstein transform of X relative to a closed substack C ⊂ X to be the complement of the strict transform of the saturation o...
Matrix factorizations and singularity categories for stacks
Matrix factorizations singularity categories for stacks
2010/11/23
We study matrix factorizations of a section W of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with...
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, ...
Representation stacks, D-branes and noncommutative geometry
Representation stacks D-branes noncommutative geometry
2010/12/13
n this note we prove that the spec(C)-points of the representation Artin-stack [repnR/PGLn] of n-dimensional representations of an affine C-algebra R correspond to C-algebra morphisms R - An where An ...
Derived Resolution Property for Stacks, Euler Classes and Applications
Derived Resolution Property for Stacks Euler Classes Applications
2010/12/13
By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in P4. These numbers are...
Decomposition Theorem for Perverse sheaves on Artin stacks
Decomposition Theorem Perverse sheaves Artin stacks
2010/12/10
We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine automorphism groups over finite fields and over the complex numbers. During the proof, we also give the generic...